PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions

Evaluate the following:

i⁴⁵⁷

Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? 

Evaluate the following:

(ii) i⁵²⁸

Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? 

Evaluate the following:

 \[\frac{1}{i^{58}}\]

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]

Evaluate the following:

\[i^{37} + \frac{1}{i^{67}}\].

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? \[\left\{ 1 \right\} \in A\]

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[2 \subset A\]

Evaluate the following:

\[\left( i^{41} + \frac{1}{i^{257}} \right)^9\]

Evaluate the following:

\[( i^{77} + i^{70} + i^{87} + i^{414} )^3\]

Evaluate the following:

 \[i^{30} + i^{40} + i^{60}\]

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\] 

Evaluate the following:

\[i^{49} + i^{68} + i^{89} + i^{110}\]

Let \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\] Which of the following are true? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]

Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true?\[\left\{ \left\{ \phi \right\} \right\} \subset A\]

Show that 1 + i¹⁰ + i²⁰ + i³⁰ is a real number.

Write down all possible subsets of each of the following set: 

 {a} 

Write down all possible subsets of each of the following set: 

 {0, 1}, 

Write down all possible subsets of each of the following set: 

{a, b, c},